cosinusprod_error_hdg.cc

The sinus product function – error analysis for the hybrid discontinuous Galerkin method

#include "rheolef.h"
using namespace rheolef;
using namespace std;
#include "cosinusprod.h"
#include "cosinusprod_grad.h"
int main(int argc, char**argv) {
environment rheolef(argc, argv);
Float err_linf_expected = (argc > 1) ? atof(argv[1]) : 1e+38;
bool with_sigma = (argc <= 2) || argv[2] != string("-no-sigma");
field uh, lambda_h, sigma_h;
din >> catchmark("u") >> uh
>> catchmark("lambda") >> lambda_h;
if (with_sigma) {
din >> catchmark("sigma") >> sigma_h;
}
space Xh = uh.get_space();
geo omega = Xh.get_geo();
size_t k = Xh.degree();
size_t d = omega.dimension();
integrate_option iopt;
iopt.set_family(integrate_option::gauss);
iopt.set_order(3*(k+1)+4);
Float err_u_l2 = sqrt(integrate (omega, sqr(uh-u_exact(d)), iopt));
string opts = Xh.get_basis().option().stamp();
space Xh1 (omega, "P"+itos(k+1)+"d"+opts);
field euh = interpolate (Xh1, uh-u_exact(d));
Float err_u_linf = euh.max_abs();
Float err_u_h1 = sqrt(integrate (omega, norm2(grad_h(euh)), iopt)
+ integrate (omega.sides(), (1/h_local())*sqr(jump(euh)), iopt));
derr << "err_u_l2 = " << err_u_l2 << endl
<< "err_u_linf = " << err_u_linf << endl
<< "err_u_h1 = " << err_u_h1 << endl;
if (with_sigma) {
Float err_sigma_l2 = sqrt(integrate (omega, norm2(sigma_h-grad_u(d)), iopt));
space Th1 (omega, "P"+itos(k+1)+"d"+opts, "vector");
field esh = interpolate (Th1, sigma_h-grad_u(d));
Float err_sigma_linf = esh.max_abs();
derr << "err_sigma_l2 = " << err_sigma_l2 << endl
<< "err_sigma_linf = " << err_sigma_linf << endl;
}
if (!lambda_h.get_space().get_basis().option().is_restricted_to_sides()) {
space Mh = lambda_h.get_space();
trial lambda(Mh); test mu(Mh);
form ms = integrate(lambda*mu);
field kh = integrate(u_exact(d)*mu, iopt);
field ph_lambda(Mh);
problem pms (ms);
pms.solve (kh, ph_lambda);
Float err_lambda_l2 = sqrt(integrate (omega["sides"], h_local()*sqr(lambda_h-ph_lambda), iopt));
derr << "err_lambda_l2 = " << err_lambda_l2 << endl;
}
return (err_u_linf <= err_linf_expected) ? 0 : 1;
}
Float
see the Float page for the full documentation
field
see the field page for the full documentation
form
see the form page for the full documentation
geo
see the geo page for the full documentation
problem
see the problem page for the full documentation
rheolef::integrate_option::gauss
@ gauss
Definition: integrate_option.h:132
rheolef::din
idiststream din
see the diststream page for the full documentation
Definition: diststream.h:427
rheolef::derr
odiststream derr(cerr)
see the diststream page for the full documentation
Definition: diststream.h:436
space
see the space page for the full documentation
test
see the test page for the full documentation
trial
see the test page for the full documentation
cosinusprod.h
The cosinus product function.
main
int main(int argc, char **argv)
Definition: cosinusprod_error_hdg.cc:30
cosinusprod_grad.h
The cosinus product function – its gradient.
Xh1
space_basic< T, M > Xh1
Definition: field_expr.h:263
mkgeo_ball.d
int d
Definition: mkgeo_ball.sh:154
mkgeo_contraction.mu
mu
Definition: mkgeo_contraction.sh:193
rheolef
This file is part of Rheolef.
Definition: compiler_eigen.h:37
rheolef::h_local
details::field_expr_v2_nonlinear_terminal_function< details::h_local_pseudo_function< Float > > h_local()
h_local: see the expression page for the full documentation
Definition: field_expr_terminal.h:527
rheolef::grad_h
std::enable_if< details::is_field_convertible< Expr >::value,details::field_expr_v2_nonlinear_terminal_field< typename Expr::scalar_type,typename Expr::memory_type,details::differentiate_option::gradient >>::type grad_h(const Expr &expr)
grad_h(uh): see the expression page for the full documentation
Definition: field_expr_terminal.h:949
rheolef::integrate
std::enable_if< details::is_field_expr_v2_nonlinear_arg< Expr >::value &&! is_undeterminated< Result >::value, Result >::type integrate(const geo_basic< T, M > &omega, const Expr &expr, const integrate_option &iopt, Result dummy=Result())
see the integrate page for the full documentation
Definition: integrate.h:202
rheolef::interpolate
field_basic< T, M > interpolate(const space_basic< T, M > &V2h, const field_basic< T, M > &u1h)
see the interpolate page for the full documentation
Definition: interpolate.cc:233
rheolef::norm2
T norm2(const vec< T, M > &x)
norm2(x): see the expression page for the full documentation
Definition: vec.h:379
rheolef::itos
std::string itos(std::string::size_type i)
itos: see the rheostream page for the full documentation
rheolef.h
rheolef - reference manual
lambda
Definition: yield_slip_circle.h:34
u_exact
g u_exact
Definition: taylor_exact.h:26
grad_u
tensor grad_u
Definition: transport_tensor_exact.icc:26